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Examining Monotonicity and Saliency Using Level- k Reasoning in a Voting Game

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  • Anna Bassi

    (Department of Political Science, University of North Carolina at Chapel Hill, 361 Hamilton Hall, CB 3265, UNC-CH, Chapel Hill, NC 27599-3265, USA)

  • Kenneth C. Williams

    (Department of Political Science, Michigan State University, 303 South Kedzie Hall, Michigan State University, East Lansing, MI 48824, USA)

Abstract

This paper presents an experiment that evaluates the effect of financial incentives and complexity in political science voting experiments. To evaluate the effect of complexity we adopt a level- k reasoning model concept. This model by Nagel [1] postulates that players might be of different types, each corresponding to the level of reasoning in which they engage. Furthermore, to postulate the effect of financial incentives on subjects’ choice, we used the Quantal Response Equilibrium (QRE) concept. In a QRE, players’ decisions are noisy, with the probability of playing a given strategy increasing in its expected payoff. Hence, the choice probability is a function of the magnitude of the financial incentives. Our results show that low complexity promotes the highest degree of level- k strategic reasoning in every payment treatment. Standard financial incentives are enough to induce equilibrium behavior, and the marginal effect of extra incentives on equilibrium behavior seems to be negligible. High complexity, instead, decreases the rate of convergence to equilibrium play. With a sufficiently high complexity, increasing payoff amounts does promote more strategic behavior in a significant manner. Our results show with complex voting games, higher financial incentives are required for the subjects to exert the effort needed to complete the task.

Suggested Citation

  • Anna Bassi & Kenneth C. Williams, 2014. "Examining Monotonicity and Saliency Using Level- k Reasoning in a Voting Game," Games, MDPI, vol. 5(1), pages 1-27, February.
    • Handle: RePEc:gam:jgames:v:5:y:2014:i:1:p:26-52:d:32962
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    as
    1. Gneezy, Uri & Rustichini, Aldo, 2000. "A Fine is a Price," The Journal of Legal Studies, University of Chicago Press, vol. 29(1), pages 1-17, January.
    2. Camerer, Colin F & Hogarth, Robin M, 1999. "The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework," Journal of Risk and Uncertainty, Springer, vol. 19(1-3), pages 7-42, December.
    3. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    4. Brekke, Kjell Arne & Kverndokk, Snorre & Nyborg, Karine, 2003. "An economic model of moral motivation," Journal of Public Economics, Elsevier, vol. 87(9-10), pages 1967-1983, September.
    5. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    6. Arkes, Hal R. & Dawes, Robyn M. & Christensen, Caryn, 1986. "Factors influencing the use of a decision rule in a probabilistic task," Organizational Behavior and Human Decision Processes, Elsevier, vol. 37(1), pages 93-110, February.
    7. Matthias Messner & Mattias Polborn, 2007. "Strong and coalition-proof political equilibria under plurality and runoff rule," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(2), pages 287-314, January.
    8. Min Ding & Rajdeep Grewal & John Liechty, 2005. "Incentive-aligned conjoint analysis," Framed Field Experiments 00139, The Field Experiments Website.
    9. Markus Prior & Arthur Lupia, 2005. "What Citizens Know Depends on How You Ask Them: Experiments on Time, Money and Political Knowledge," Experimental 0510001, University Library of Munich, Germany.
    10. Franziska Voelckner, 2006. "An empirical comparison of methods for measuring consumers’ willingness to pay," Marketing Letters, Springer, vol. 17(2), pages 137-149, April.
    11. Kormendi, Roger C. & Plott, Charles R., 1982. "Committee decisions under alternative procedural rules : An experimental study applying a new non-monetary method of preference inducement," Journal of Economic Behavior & Organization, Elsevier, vol. 3(2-3), pages 175-195.
    12. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    13. Smith, Vernon L, 1976. "Experimental Economics: Induced Value Theory," American Economic Review, American Economic Association, vol. 66(2), pages 274-279, May.
    14. James, Harvey Jr., 2005. "Why did you do that? An economic examination of the effect of extrinsic compensation on intrinsic motivation and performance," Journal of Economic Psychology, Elsevier, vol. 26(4), pages 549-566, August.
    15. Uri Gneezy & Aldo Rustichini, 2000. "Pay Enough or Don't Pay at All," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(3), pages 791-810.
    16. Richard D. Mckelvey & Thomas R. Palfrey, 1996. "A Statistical Theory Of Equilibrium In Games," The Japanese Economic Review, Japanese Economic Association, vol. 47(2), pages 186-209, June.
    17. Sugato Dasgupta & Kirk Randazzo & Reginald Sheehan & Kenneth Williams, 2008. "Coordinated voting in sequential and simultaneous elections: some experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 11(4), pages 315-335, December.
    18. Rydval, Ondrej & Ortmann, Andreas, 2004. "How financial incentives and cognitive abilities affect task performance in laboratory settings: an illustration," Economics Letters, Elsevier, vol. 85(3), pages 315-320, December.
    19. John A. List & David Lucking-Reiley, 2002. "Bidding Behavior and Decision Costs in Field Experiments," Economic Inquiry, Western Economic Association International, vol. 40(4), pages 611-619, October.
    20. Roland Bénabou & Jean Tirole, 2003. "Intrinsic and Extrinsic Motivation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(3), pages 489-520.
    21. Erik Hoelzl & Aldo Rustichini, 2005. "Overconfident: Do You Put Your Money On It?," Economic Journal, Royal Economic Society, vol. 115(503), pages 305-318, April.
    22. Yaron Azrieli & Christopher P. Chambers & Paul J. Healy, 2018. "Incentives in Experiments: A Theoretical Analysis," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1472-1503.
    23. Shapiro, Dmitry & Shi, Xianwen & Zillante, Artie, 2014. "Level-k reasoning in a generalized beauty contest," Games and Economic Behavior, Elsevier, vol. 86(C), pages 308-329.
    24. John A. List, 2001. "Do Explicit Warnings Eliminate the Hypothetical Bias in Elicitation Procedures? Evidence from Field Auctions for Sportscards," American Economic Review, American Economic Association, vol. 91(5), pages 1498-1507, December.
    25. Smith, Vernon L & Walker, James M, 1993. "Monetary Rewards and Decision Cost in Experimental Economics," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 245-261, April.
    26. Williams, Kenneth, 2013. "Introduction to Game Theory: A Behavioral Approach: International Edition," OUP Catalogue, Oxford University Press, number 9780199837410.
    27. Smith, Vernon L, 1982. "Microeconomic Systems as an Experimental Science," American Economic Review, American Economic Association, vol. 72(5), pages 923-955, December.
    28. Friedman,Daniel & Sunder,Shyam, 1994. "Experimental Methods," Cambridge Books, Cambridge University Press, number 9780521456821.
    29. List, John A & Shogren, Jason F, 1998. "The Deadweight Loss of Christmas: Comment," American Economic Review, American Economic Association, vol. 88(5), pages 1350-1355, December.
    30. Wilcox, Nathaniel T, 1993. "Lottery Choice: Incentives, Complexity and Decision Time," Economic Journal, Royal Economic Society, vol. 103(421), pages 1397-1417, November.
    31. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    32. Wright, William F. & Aboul-Ezz, Mohamed E., 1988. "Effects of extrinsic incentives on the quality of frequency assessments," Organizational Behavior and Human Decision Processes, Elsevier, vol. 41(2), pages 143-152, April.
    33. Guala,Francesco, 2005. "The Methodology of Experimental Economics," Cambridge Books, Cambridge University Press, number 9780521618618.
    34. Lorenzo Cappellari & Gilberto Turati, 2004. "Volunteer Labour Supply: the role of workers’ motivations," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 75(4), pages 619-643, December.
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